Measurement · SHS2 Mathematics

Lesson notes

Learning Objectives

Indicator: 2.3.2.LI.3 - Solve real world problems that involve the volume/capacity of a 3-D object.

By the end of the lesson, learners can:

Identify the appropriate volume formula for a given 3-D object (cube, rectangular prism, or cylinder) in a real-world problem.
Convert measurements between SI units (cm, m, mm) and imperial units (inches, feet, yards) as needed before calculating volume.
Solve multi-step word problems involving volume of cubes, rectangular prisms and cylinders, including problems requiring proportional reasoning.
Apply the concept of capacity (e.g., gallons, litres) when solving problems about how much liquid a container can hold, given a conversion factor.
Determine the cost of materials or the value of contents based on the volume of a 3-D object.

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Curriculum details

Strand: Geometry Around Us (Strand 3)
Sub-strand: Measurement (3.2)
Content standard: 2.3.2.CS.3 - Demonstrate conceptual understanding of the measurement of surface area, volume and capacity of solid shapes. 2.3.2.LO.3 Determine the volume and capacity of solid shapes and Solve problems that involve SI and imperial units in surface area, volume and capacity measurements.
Indicator: 2.3.2.LI.3 - Solve real world problems that involve the volume/capacity of a 3-D object.
Suggested placement: Semester 2, Week 11 (Week 31 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Curriculum reference: NaCCA curriculum document, p. 261

Exemplars (from the NaCCA curriculum)

Collaborative learning: Learners discuss and solve real world problems on volume. While they experience this concept, model tolerance among learners by creating opportunities for Collaborative Learning through mixed-ability grouping.
Example 1: Ewuradwoa wants to drink milk from a glass that is in the shape of a cylinder. The height of the glass is 15 units, and the radius of the base is 3 units. What is the quantity (volume) of milk that she requires to fill the glass completely?
Solution: Given that, the height of the glass = 15 units and the radius of the base = 3 units. To find the volume of the glass, we need to use the formula for the volume of a cylinder, which is πr 2 h cubic units. The volume of the glass, V = πr 2 h V = π × (3 2 ) × 15
V = π × 135 V = 423.9 cubic units. Therefore, she needs approximately 424 cubic units of milk to fill her glass.
Example 2: The pedestal on which a statue is raised is a rectangular concrete solid measuring 9 feet long, 9 feet wide and 6 inches high. How much is the cost of the concrete in the pedestal if concrete costs GH70 per cubic yard?
Solution: We need to find the volume of the pedestal in cubic yards and then multiply it by the cost factor of GHC70 per cubic yard. Recall the general formula for computing the volume of a rectangular solid: V = LWH. In this case, L = 9 feet, W = 9 feet and H = 6 inches. Since we want to compute volume in cubic yards, we should convert all three measurements to yards before using the formula for volume. To convert from feet to yards, we divide by 3; to convert from inches to yards, we divide by 36.
L = 9 feet = (9/3) yards = 3 yards W = 9 feet = (9/3) yards = 3 yards H = 6 inches = (6/36) yards = 1/6 yards Now we compute the volume: Volume = (3 yards) (3 yards)(1/6 yards) = 9/6 cubic yards = 1.5 cubic yards Finally, we multiply by the cost factor: Cost = (1.5 cu yd)(GH70 per cu yd) = GHC105
Example 3: Ampofo loves playing with building blocks. He has built a structure with 15 cubic blocks. If the edge of each cube is 3in, what would be the volume of his structure?
Solution: Let's calculate the volume of one cube. The volume of cube = Edge × Edge × Edge = 3 in × 3 in × 3 in =27 in 3 There are 15 cubes in his structure. So, the volume of the structure is, Volume of structure =15 × Volume of one cube = 15 × 27 in 3 = 405 in 3 Therefore, the volume of the structure is 405 in 3 .
Examples: i. Ananga has a rectangular aquarium that is 12 inches long, 8 inches wide and 8 inches high, providing enough room to safely house 6 guppies. Assuming that the number of guppies that can
be safely housed depends upon the size of the aquarium, how many guppies can be safely housed in an aquarium that is 24 inches long, 16 inches wide and 16 inches high? ii. Adobe is digging a hole for a rectangular swimming pool measuring 38 feet long by 22 feet wide by 8 feet deep. How much water will the swimming pool hold, assuming that 1 cubic foot = 7.5 gallons iii. A cylindrical can that is four inches tall and has a radius of 1.5 inches can hold 10¢ worth of soda. Assuming that the value of the contents is proportional to the size (volume) of the can, what would be the value of the soda contained in a can that is 8 inches tall with a radius of 3 inches?
Teaching and Learning Resources:
- Mathematical sets.
- Technology tools such as computers, mobile phones, etc.
- * Computer software applications like GeoGebra
Assessment (2.3.2.AS.3). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning.